Non-linearity in dipolar solvation dynamics in water-ethanol mixture: Composition dependence of free energy landscape

Liquid mixtures of water and amphiphilic solutes exhibit a string of yet unexplained anomalies in the low cosolvent (or solute) concentration regime. Among such solutions, mixtures of water and ethanol stand out for their distinctive role in biology. We study, in this binary mixture, the composition dependent difference between the nonequilibrium and the equilibrium solvent responses to a dipolar probe indole in the low-to-intermediate concentration regime. The usually employed linear response formalism seems to break down at low ethanol concentration. The nonequilibrium solvent response is particularly different from that of the equilibrium solvent response in the concentration (x_EtOH) between 0.07 and 0.12. We introduce an order parameter in terms of the changing local composition at the nearest neighbor separation. This order parameter captures the anomalies faithfully. The anomalies are seen to arise from a competition between hydrophilic and hydrophobic interactions and are most prominent at the small-to-intermediate length scale. We attempt to rationalize the results in terms of a composition dependent free energy length scale.